Many people show an intrinsic bias in visuospatial processing called pseudoneglect – some are better at processing objects to the right, whereas others are biased to the left. We measured pseudoneglect in neurotypical participants using a variant of the line bisection task. In the same participants, we measured performance in a social cognition task. This theory of mind task measured whether each participant had a processing-speed bias toward the right of, or left of, a cartoon agent about which the participant was thinking. Crucially, the cartoon was rotated such that what was left and right with respect to the cartoon was up and down with respect to the participant. Thus, a person's own left-right bias could not align directly onto left and right with respect to the cartoon head. Performance on the two tasks was significantly correlated. People who had a natural bias toward processing their own left side of space were quicker to process how the cartoon might think about objects to the left side of its face, and likewise for a rightward bias. One possible interpretation of these results is that the act of processing one's own personal space, and the act of reconstructing someone else's processing of their space, uses at least partially shared mechanisms.